CHAPTER I. ADDITION AND RESOLUTION OF VECTORS. 3. Scalar and Vector Magnitudes.— Physical magnitudes may be divided into two classes according to whether they have the property of orientation or not. Magnitudes which have direction are called vectors, while those which do not have this property are called scalars. Displacement, velocity, acceleration, force, torque, and momentum are vector magnitudes. Mass, density, work, energy, and time are scalars. 4. Graphical Representation of Vectors. — Vectors are represented by directed lines or arrows. The length of the directed line represents the magnitude of the vector, while its direction coincides with that of the vector. For brevity the directed lines as well as the physical quantities which they represent are called vectors. The head and the tail of the directed line are called, respectively, the terminus and the origin of the vector. In Fig. 1, for instance, P is the origin and Q the terminus of the vector a. 6. Notation. — Vectors will be denoted by letters printed in Gothic type, while their magnitudes will be represented by the same letters printed in italic type. Thus in Fig. 1 the vector PQ is denoted by a, but if it is desired to represent the length PQ without regard to its orientation a is used. 6. Equal Vectors. — Two vectors are said to be equal if they have the same length and the same direction. It follows, th&t t.VlA Vfl.lllA nf a VAnf.AT* ia •n/vf /»"hannMa/1 wl-^^ i* o FIG. 1.